Which of the following numbers is a multiple of 6? ${60,74,85,95,106}$
Explanation: The multiples of $6$ are $6$ $12$ $18$ $24$ ..... In general, any number that leaves no remainder when divided by $6$ is considered a multiple of $6$ We can start by dividing each of our answer choices by $6$ $60 \div 6 = 10$ $74 \div 6 = 12\text{ R }2$ $85 \div 6 = 14\text{ R }1$ $95 \div 6 = 15\text{ R }5$ $106 \div 6 = 17\text{ R }4$ The only answer choice that leaves no remainder after the division is $60$ $ 10$ $6$ $60$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $6$ are contained within the prime factors of $60$ $60 = 2\times2\times3\times5 6 = 2\times3$ Therefore the only multiple of $6$ out of our choices is $60$. We can say that $60$ is divisible by $6$.